Cook the croquettes: Fill the skillet with about 1/4 inch of oil and heat until shimmering over medium high heat. Add the croquettes and shallow fry in the hot oil until well browned and hot all the way through, 6-8 minutes total.
My husband found the shallots in the vinaigrette to be a bit strong. I thought they were perfect. If you love shallots, add the full amount. If not, add just a bit. You can always add more, but it's hard to take them out.